A certain type of electronic component has a lifetime Y (in hours) with probability density function given by
A certain type of electronic component has a lifetime Y (in hours) with probability density function given by
That is, Y has a gamma distribution with parameters α = 2 and θ. Let 
denote the MLE of θ. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours.
a Find the MLE of θ.
b Find E() and V(
).
c Suppose that actually equals 130. Give an approximate bound that you might expect for the error of estimation.
d What is the MLE for the variance of Y?
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A certain type of electronic component has a lifetime Y (in hours) with probability density function given by
2. A certain type of electronic component has a lifetime X (in hours) with probability density...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2)...
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2) (a) Using Chebyshev's Inequality, find a lower bound on the probability that the lifetimes are within 20 hours of the mean (b) Suppose it is found that the lifetimes actually follow an exponential distribution Determine the eract probability that the lifetimes are within 20 hours of the mean
2) The lifetime in years of a certain type of electronic component has a probability density...
2) The lifetime in years of a certain type of electronic component has a probability density function given by: otherwise a) If the expected value of the random variable is 3/5 i.e. E(X)-3/5, find a and b. b) Show that the median lifetime is approximately 0.6501 years.
The probability density function of X, the lifetime of a certain type of electronic device (measured...
The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by fX(x) = ( C/x^2 x>5 0 x<5 where C>0 is a constant which needs to be determined. (i) What is the probability that the device’s lifetime is 10 hours? (ii) Find the 25%th quantile of X? (iii) If the device lifetime is X, then its total electricity cost equals . What is the expected total electricity cost of the...
QUESTION 1 The length of life of an electronic component used in a guidance control system...
QUESTION 1 The length of life of an electronic component used in a guidance control system for missiles is assumed to follow a Weibull distribution with density given by >0, θ > 0 Let Yı,Y2, ,Y10 denote a random variables for the lifetime of a sample of size n= 10 of these electronic components. We wish to construct a 95% confidence interval for θ (a) Find the maximum likelihood estimator, 6, of 0. (b) Find the distribution of U =...
You are given the following probability density function, 6x(r), for the cosine of the surface an...
You are given the following probability density function, 6x(r), for the cosine of the surface angle, S, of a laser etching tool. The distribution function has one parameter, a, and one constant, c. -1sxs1 a) What is the value of the constant, e? b) What is the moment estimator for a? c) Explain how you can determine if this moment estimator is unbiased. t... . 24) denote a random sample of sample size n 24 with sample mean of-0.01 and...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2) (a) Using Chebyshev's Inequality, find a lower bound on the probability that the lifetimes are within 20 hours of the mean (b) Suppose it is found that the lifetimes actually follow an exponential distribution Determine the eract probability that the lifetimes are within 20 hours of the mean
2) The lifetime in years of a certain type of electronic component has a probability density function given by: otherwise a) If the expected value of the random variable is 3/5 i.e. E(X)-3/5, find a and b. b) Show that the median lifetime is approximately 0.6501 years.
QUESTION 1 The length of life of an electronic component used in a guidance control system for missiles is assumed to follow a Weibull distribution with density given by >0, θ > 0 Let Yı,Y2, ,Y10 denote a random variables for the lifetime of a sample of size n= 10 of these electronic components. We wish to construct a 95% confidence interval for θ (a) Find the maximum likelihood estimator, 6, of 0. (b) Find the distribution of U =...
You are given the following probability density function, 6x(r), for the cosine of the surface angle, S, of a laser etching tool. The distribution function has one parameter, a, and one constant, c. -1sxs1 a) What is the value of the constant, e? b) What is the moment estimator for a? c) Explain how you can determine if this moment estimator is unbiased. t... . 24) denote a random sample of sample size n 24 with sample mean of-0.01 and...
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